IRR is the rate at which every cash flow discounts back to zero. It is the right tool for irregular timings, and it systematically flatters anything held briefly.
14 min read · Level 4
IRR gets criticised for its reinvestment assumption, and the criticism is usually aimed at the wrong target. The arithmetic assumes nothing; it is a root of a polynomial, and the equation is as true as any equation. What smuggles the assumption in is the act of quoting a rate as though it described an investor's year, when it describes only the interval in which the capital happened to be working. That distinction has a sharp practical consequence, because the easiest way to raise a measured IRR is not to make a better investment but to shorten the period - exit sooner, return capital earlier, borrow at the fund level so the money is called later. Every one of those is legitimate, is visible in the cash flows, and moves the headline figure without the underlying asset behaving any differently. If that is right, then a strong IRR beside a thin multiple is not evidence of skill at investing. It is evidence of skill at cash-flow timing, which is a real and valuable capability, and is simply not the one most people believe they are buying.
The internal rate of return is the single annual rate at which the present value of everything you receive exactly equals the present value of everything you pay. Formally, it is the rate r that solves
sum over t of CF_t / (1 + r)^t = 0
where CF_t is the cash flow at time t, negative when money goes out and positive when it comes in.
There is no formula that isolates r. It is found by trying rates until the sum is zero, which is what every spreadsheet function is doing behind the label. That matters, because it means IRR is defined by the cash flows and nothing else: change one date by three months and the answer changes, with no other input touched.
It is the only common measure that handles money going in and out at irregular intervals, which is why private markets, property and project finance all quote it. And because it is a rate rather than an amount, it is silent about size - which is the source of nearly every misuse.
Because ROI cannot cope with the shape of a real investment. Money goes in once, then again for a refurbishment; income arrives quarterly; a partial sale returns some capital in year three; the rest exits in year five. There is no meaningful denominator for a simple percentage, and IRR is what answers the question anyway.
And because it is the number that most decisions in private markets are actually argued in. Understanding what it assumes is therefore not an academic nicety - it is the difference between reading a 30% IRR as an achievement and reading it as a statement about how briefly the money was at work.
Educational, not personalised financial advice. Nothing in the Investor Academy is a recommendation to buy, sell or hold anything — what is right for you depends on your own circumstances and the rules where you live.
A deal with a realistic shape. Put in 250,000 at the start. Receive 18,000 at the end of years one and two, 20,000 at the end of years three and four, and 330,000 at the end of year five when it is sold.
t=0 -250,000 t=1 +18,000 t=2 +18,000 t=3 +20,000 t=4 +20,000 t=5 +330,000
Total received is 406,000, so the gain is 156,000 and the simple ROI is 62.4%. The IRR - the rate solving the equation above - is 11.45%. Check it if you like: discount those five inflows at 11.446939% and they sum to 250,000.
Now the two things worth understanding.
First, timing changes the answer even when the total does not. Compare two investments that each return exactly 150,000 on 100,000.
P: -100,000 at t=0, then nothing until +150,000 at t=5. Q: -100,000 at t=0, then +10,000 at the end of each of years one to four, and +110,000 at t=5.
Both return 150,000 in total. P's IRR is 1.5 to the power of one-fifth, minus one, which is 8.45%. Q's IRR is exactly 10.00%, because Q is the cash-flow shape of a bond paying 10% on par. Identical money, 1.55 percentage points of difference, produced entirely by Q returning some of it earlier.
Second, and this is the one that misleads people: IRR flatters short holds, because annualising a short period compounds it. An investment that turns 100,000 into 118,000 in four months has made 18,000. Annualised, that is 1.18 to the power of three, minus one, which is 64.30%.
That 64.30% is a true statement of what the rate was while the money was working. It is not a statement about a year. Doing the deal once and holding cash for the other eight months leaves you with 118,000 at the end of the year, which is 18.0%. The 64.30% is precisely the figure you would achieve if you could do the same thing three times consecutively with everything reinvested - 100,000 times 1.18 cubed is 164,303.20 - and whether that is available is a question about the world, not about the arithmetic.
Set it against a duller deal: 250,000 growing to 650,000 over seven years is a multiple of 2.60 and an IRR of 14.63%. The four-month deal has an IRR more than four times higher and made 18,000. The seven-year deal made 400,000. Both figures are correct; only one of them is money.
The first mistake is treating IRR as a prediction of what a year will look like. It is the rate while the capital was deployed, and unless the capital is immediately redeployed at the same rate, the year will not resemble it.
The second is comparing IRRs across very different durations without asking what happened to the money afterwards. A 64% IRR over four months and a 15% IRR over seven years are answers to different questions, and the shorter one carries an unstated assumption about reinvestment that nobody has committed to.
The third is forgetting that IRR says nothing about size. It is a rate, so a deal that earns 64% on 20,000 outranks one earning 15% on 2,000,000 on this measure alone, which is why no serious process uses IRR by itself.
The fourth is manufacturing an IRR by moving cash flows rather than by creating value. Returning capital early, using borrowing at the fund level to delay calling money, or timing a distribution before a year end all raise the measured IRR without changing what the underlying asset produced.
The fifth is quoting an IRR on a position that has not been sold. The final cash flow in that calculation is a valuation somebody chose, and an IRR resting on an estimated exit is a forecast wearing the clothes of a result.
Date and amount, signed, including every cost. The IRR is entirely determined by this list, so an error here cannot be detected anywhere downstream - the answer will simply be wrong and will look exactly as convincing as a right one.
Take the rate you were given and discount every cash flow at it. The sum should be zero. This takes a minute and it is the only check that does not rely on trusting whoever built the model.
'11.45% over five years' and '64.30% over four months' are the complete statements. An IRR without its duration is the single most misleading figure in this subject, and the duration is what tells the reader how much reinvestment assumption is hiding inside it.
Alongside every IRR, write the absolute gain. 156,000 on 250,000. 18,000 on 100,000. Rates decide which opportunity is better per unit of capital per unit of time; amounts are what you actually end up with, and one line prevents the two from being confused.
An IRR is achievable in practice only if returned capital goes back to work at a similar rate. Write down where the money would actually go - another deal, cash, a repayment - and for how long it sits idle. That sentence is the difference between the arithmetic and the outcome.
Compare the IRR with the multiple. Where the IRR is strong and the multiple is thin, the return came from speed rather than from value - which may be entirely legitimate, and is a different business with different risks from one that compounds capital over years.
Wherever cash moves in and out at irregular times: private deals, property with a refurbishment, project finance, anything with partial exits or capital calls.
Avoid it as a single comparison measure between holdings of very different duration, avoid it where you cannot say what the returned capital did next, and treat any IRR containing an unrealised exit value as a forecast rather than a result.
In private markets a return is frequently quoted while the underlying asset is still held, which means the final and largest cash flow in the calculation is a valuation rather than a receipt. Because that valuation sits at the end of the series and is much the biggest number in it, the whole rate is extremely sensitive to it - and the party producing the valuation is the same party quoting the rate. Nothing about the arithmetic is wrong, and the figure will still be described as a return rather than as a forecast, because there is no established vocabulary that distinguishes the two.
Ask which cash flows in a quoted IRR have actually happened. A rate whose largest input is an estimate is a projection, and it should be read with the same scepticism as any other forecast of a single number.
A fund can report a return measured from the day money was called from investors, or from the day the fund began, or with a credit facility used to defer the call. All three are defensible, all three are computed correctly, and they can differ by several percentage points on identical underlying assets, because each changes how long investor capital was recorded as being at work. The differences do not show up in the multiple, which is one reason multiple and rate are conventionally quoted together.
When an IRR is quoted, ask from what date it is measured and whether any borrowing delayed the capital calls. Those two questions reconcile most differences between figures that both appear to describe the same thing.
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